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Summary

With special relation to smart grids, this book provides clear and comprehensive explanation of how Digital Signal Processing (DSP) and Computational Intelligence (CI) techniques can be applied to solve problems in the power system.

Its unique coverage bridges the gap between DSP, electrical power and energy engineering systems, showing many different techniques applied to typical and expected system conditions with practical power system examples.

Surveying all recent advances on DSP for power systems, this book enables engineers and researchers to understand the current state of the art and to develop new tools. It presents:

an overview on the power system and electric signals, with description of the basic concepts of DSP commonly found in power system problems

the application of several signal processing tools to problems, looking at power signal estimation and decomposition, pattern recognition techniques, detection of the power system signal variations

description of DSP in relation to measurements, power quality, monitoring, protection and control, and wide area monitoring

a companion website with real signal data, several Matlab codes with examples, DSP scripts and samples of signals for further processing, understanding and analysis

Practicing power systems engineers and utility engineers will find this book invaluable, as will researchers of electrical power and energy systems, postgraduate electrical engineering students, and staff at utility companies.

Author Biography

Professor Paulo F. Ribeiro, Calvin College, USA

Professor Ribeiro is professor of Engineering at Calvin College, Michigan. He has been involved with the application of advanced signal processing, applied to power quality and power systems in general, for the past fifteen years. For the past six years he has chaired the IEEE Task Force on Probabilistic Aspects of Harmonics. In 1994 he proposed the use of wallets to power quality applications; this has been followed by many people and has generated much research, several Masters and a PhD Thesis. Dr. Ribeiro is active in the IEEE, CIGRE and IEC working groups on power quality, and is a Registered Professional Engineer in the State of Iowa.

Table of Contents

About the Authors xiii

Preface xv

AccompanyingWebsite xxi

Acknowledgments xxiii

1 Introduction 1

1.1 Introduction 1

1.2 The Future Grid 2

1.3 Motivation and Objectives 3

1.4 Signal Processing Framework 4

1.5 Conclusions 8

References 10

2 Power Systems and Signal Processing 11

2.1 Introduction 11

2.2 Dynamic Overvoltage 12

2.2.1 Sustained Overvoltage 12

2.2.2 Lightning Surge 13

2.2.3 Switching Surges 15

2.2.4 Switching of Capacitor Banks 17

2.3 Fault Current and DC Component 21

2.4 Voltage Sags and Voltage Swells 25

2.5 Voltage Fluctuations 27

2.6 Voltage and Current Imbalance 29

2.7 Harmonics and Interharmonics 29

2.8 Inrush Current in Power Transformers 42

2.9 Over-Excitation of Transformers 45

2.10 Transients in Instrument Transformers 47

2.10.1 Current Transformer (CT) Saturation (Protection Services) 47

2.10.2 Capacitive Voltage Transformer (CVT) Transients 54

2.11 Ferroresonance 55

2.12 Frequency Variation 56

2.13 Other Kinds of Phenomena and their Signals 56

2.14 Conclusions 57

References 58

3 Transducers and Acquisition Systems 59

3.1 Introduction 59

3.2 Voltage Transformers (VTs) 60

3.3 Capacitor Voltage Transformers 64

3.4 Current Transformers 67

3.5 Non-Conventional Transducers 71

3.5.1 Resistive Voltage Divider 71

3.5.2 Optical Voltage Transducer 72

3.5.3 Rogowski Coil 73

3.5.4 Optical Current Transducer 74

3.6 Analog-to-Digital Conversion Processing 75

3.6.1 Supervision and Control 78

3.6.2 Protection 79

3.6.3 Power Quality 79

3.7 Mathematical Model for Noise 80

3.8 Sampling and the Anti-Aliasing Filtering 81

3.9 Sampling Rate for Power System Application 84

3.10 Smart-Grid Context and Conclusions 84

References 85

4 Discrete Transforms 87

4.1 Introduction 87

4.2 Representation of Periodic Signals using Fourier Series 87

4.2.1 Computation of Series Coefficients 90

4.2.2 The Exponential Fourier Series 92

4.2.3 Relationship between the Exponential and Trigonometric oefficients 93

4.2.4 Harmonics in Power Systems 95

4.2.5 Proprieties of a Fourier Series 97

4.3 A Fourier Transform 98

4.3.1 Introduction and Examples 98

4.3.2 Fourier Transform Properties 103

4.4 The Sampling Theorem 104

4.5 The Discrete-Time Fourier Transform 108

4.5.1 DTFT Pairs 109

4.5.2 Properties of DTFT 110

4.6 The Discrete Fourier Transform (DFT) 110

4.6.1 Sampling the Fourier Transform 116

4.6.2 Discrete Fourier Transform Theorems 116

4.7 Recursive DFT 117

4.8 Filtering Interpretation of DFT 120

4.8.1 Frequency Response of DFT Filter 123

4.8.2 Asynchronous Sampling 124

4.9 The z-Transform 126

4.9.1 Rational z-Transforms 128

4.9.2 Stability of Rational Transfer Function 131

4.9.3 Some Common z-Transform Pairs 131

4.9.4 z-Transform Properties 133

4.10 Conclusions 133

References 133

5 Basic Power Systems Signal Processing 135

5.1 Introduction 135

5.2 Linear and Time-Invariant Systems 135

5.2.1 Frequency Response of LTI System 138

5.2.2 Linear Phase FIR Filter 140

5.3 Basic Digital System and Power System Applications 142

5.3.1 Moving Average Systems: Application 142

5.3.2 RMS Estimation 144

5.3.3 Trapezoidal Integration and Bilinear Transform 146

5.3.4 Differentiators Filters: Application 148

5.3.5 Simple Differentiator 151

5.4 Parametric Filters in Power System Applications 153

5.4.1 Filter Specification 154

5.4.2 First-Order Low-Pass Filter 155

5.4.3 First-Order High-Pass Filter 155

5.4.4 Bandstop IIR Digital Filter (The Notch Filter) 156

5.4.5 Total Harmonic Distortion in Time Domain (THD) 159

5.4.6 Signal Decomposition using a Notch Filter 161

5.5 Parametric Notch FIR Filters 161

5.6 Filter Design using MATLAB1 (FIR and IIR) 163

5.7 Sine and Cosine FIR Filters 163

5.8 Smart-Grid Context and Conclusions 165

References 166

6 Multirate Systems and Sampling Alterations 167

6.1 Introduction 167

6.2 Basic Blocks for Sampling Rate Alteration 167

6.2.1 Frequency Domain Interpretation 168

6.2.2 Up-Sampling in Frequency Domain 169

6.2.3 Down-Sampling in Frequency Domain 169

6.3 The Interpolator 170

6.3.1 The Input–Output Relation for the Interpolator 172

6.3.2 Multirate System as a Time-Varying System and Nobles Identities 172

6.4 The Decimator 174

6.4.1 Introduction 174

6.4.2 The Input–Output Relation for the Decimator 174

6.5 Fractional Sampling Rate Alteration 175

6.5.1 Resampling Using MATLAB1 175

6.6 Real-Time Sampling Rate Alteration 176

6.6.1 Spline Interpolation 177

6.6.2 Cubic B-Spline Interpolation 180

6.7 Conclusions 184

References 184

7 Estimation of Electrical Parameters 185

7.1 Introduction 185

7.2 Estimation Theory 185

7.3 Least-Squares Estimator 187

7.3.1 Linear Least-Squares 188

7.4 Frequency Estimation 191

7.4.1 Frequency Estimation Based on Zero Crossing (IEC61000-4-30) 192

7.4.2 Short-Term Frequency Estimator Based on Zero Crossing 195

7.4.3 Frequency Estimation Based on Phasor Rotation 198

7.4.4 Varying the DFT Window Size 200

7.4.5 Frequency Estimation Based on LSE 201

7.4.6 IIR Notch Filter 203

7.4.7 Small Coefficient and/or Small Arithmetic Errors 203

7.5 Phasor Estimation 205

7.5.1 Introduction 205

7.5.2 The PLL Structure 207

7.5.3 Kalman Filter Estimation 209

7.5.4 Example of Phasor Estimation using Kalman Filter 211

7.6 Phasor Estimation in Presence of DC Component 212

7.6.1 Mathematical Model for the Signal in Presence of DC Decaying 213